Download free e-book on error probability in AWGN

We have quite a few articles discussing bit and symbol error rates for popular digital modulation schemes in Additive White Gaussian Noise (AWGN) channel. This post summarizes the articles discussing the theoretical and simulatederror rates for the digital modulation schemes like BPSK, QPSK, 4-PAM, 16PSK and16QAM. Further, Bit Error Rate with Gray coded mapping, bit error rate for BPSK over OFDM are also discussed.

The links to the individual articles and the Matlab/Octavesimulation models are listed below. Alternatively, I have made a e-book discussing all the below mentioned articles to a single PDF file. If you wish, you can download the free e-book by subscribing to the free email newsletter.

Please help me to understand my results.
I have simulated in Simulink (Bernoulli, Hamming Encoder, BPSK Modulator, AWGN, BPSK Demodulator, Hamming Decoder) BPSK with AWGN and have obtained that Hamming (7,4) code has lower BER than Hamming (31,26).
Is it connected with noncoherent demodulation?
I have subscribed but do not know how to get your book. Please send me the book.

can u please send me a copy of the pdf file, I really very neeeeed that!
I must simulate the OOK BER in the Nakagami-m channel(energy detection)….I really dont know how to finish it…..confluent hypergeometric function,such of things make me headache…

@lakshmi narayana: Sorry, I have not discussed CDMA scenarios in the blog. However, I would guess it will be reasonably simple to adapt the QPSK mod/demod post to the CDMA case.http://www.dsplog.com/2007/11/06/symbol-error-rate-for-4-qam/
At the transmitter, multiply each symbol by the PN chips. Correspondingly, at the receiver convolve with the PN chip and pick the maxima.

Hi Krishna,
Your blog helps me to learn OFDM , thank you very much for that.
Could you send me the download instructions ?
I am try to simulate BER for OFDM using 16QAM
I would appreciate your help.
Thanks!

hi , i hav tried qpsk with half rate convolutional coding with trellis structure of t = poly2trellis(7,[171 133]); i have also applied it with and without gray coding but still i m getting ber of 0.5.. why it does not match theoritical ber theortical ber……plzzz can any body tell me where i m wrong ….i had also tried 2/3 rate coding it works fine but ber at lower EbNo values is little bit higher after that remaining ber values are ok..but i m more intereted in 1/2 rate coding
any help will be appreciated
thanks in advance…

hi krishna,
i want to plot different modulation schemes BER vs Es/No in awgn channel on a single plot.for example, 0 to 9 db QPSK modulation, 10 to 11 db 16 QAM modulatio,12 to 19 db 32PSK modulation and so on. its output will be a single line at series of Es/No values.can u help me about this?
thnx

Hi Krishna, I am working with mobile location in IS-95 CDMA system. Could you please send me matlab simulation m-file for QPSK modulation and demodulation of Pilot signal in IS-95 CDMA for Pilot channel acquisition. It would be a great help in my research.
Best wishes,

hi,
i am working for bit error rate for BPSK, QPSK and 16 QAM modulation techniques for different code rate 1/2, 3/4, 9/16 using AWGN and Rayleigh channel so plz help me for changing code rate and delay in hiperlan/2

I would really appreciate if you can help me to implement the cooperative communication (amplify and forward ) and (decode and forward) over the slowe fading channel . the system consistes of source, relay and destnation

Dear Mr.Krishnapillai,
I admire your dedication and sincerity in helping others by giving useful suggestions, ample guidance and valuable advises. I am doing research in communication field and topic is to improve the performance of ofdm systems. my plan is to minimise PAPR and Frequency offset by using scrambling(PAPR Redn) in Txr and Windowing in Rxr(ICI Cancellation), plz comment on this and if you have any suggestion it will defenitely help me.

@Bijunair: Well, even I have not done much on PAPR reduction rather than using scrambling at the transmitter. Am curious about how you are going to reduce the effect of frequency offset by using windowing in receiver. You may point me to some references which you are using. Thanks.

@navya: On a high level, effect of multiple access inteference is equivalent to a MIMO communication (V-BLAST) where each dimension interfers with the other. You may read more about MIMO with Zero Forcing equalizer @http://www.dsplog.com/2008/10/24/mimo-zero-forcing/

Hi, could you please send me the copy of the ebook Fundamentals of communication systems by John G. Proakis and Masoud Salehi. I’m studying communication systems and looking for some reference sources. Thanks a lot.

@Leo: Well, I do not think that Fundamentals of Communication Systems may not be available online. I can point you to another book
Signal Processing for Communications – http://www.sp4comm.org/webversion.html. Nice read.
Good luck in your studies

@ communications engineer : Typically, the e-Book is offered for subscribers who have opted in to receive posts over email. Anyhow, since you have already joined Google FriendConnect, I have send you the link over email.

Simulate 8-PSK (k = 3, M = 8) using the mapping below:
There is no need to generate individual bits. The input to the detector is r = s + n where all numbers are complex. The input, s, is a complex number with magnitude A and phase
determined by the random input. To generate complex noise, you need two independent
Gaussian random variables. Alternatively, you can model all signals as two-dimensional
vectors. The detector finds the closest signal point to r.
For this simulation, SNRb = (A^2)/6. Simulate the performance the system for SNRb = 7, 8,
9, 10, 11 dB and find the symbol and bit error rates. The printout format is:
System:8-PSK; SNRb=___(dB); #Bits transmitted=___ (i N/10, i = 1,…,10); SER=___; BER=___
Compare your results with the theoretical estimates of symbol and bit error rates. Plot the
theoretical estimates (curves) and the simulated error rates (points) in one figure.